Select units with a spatially balanced or systematic probability sample

Draws a probability sample of the units of a frame (segments, grid cells, establishments) with equal or size-proportional inclusion probabilities, within strata when given, by one of three methods:

Usage

select_units(
  frame,
  n,
  size = NULL,
  coords = NULL,
  strata = NULL,
  method = c("lpm", "systematic", "srs", "cube"),
  replicates = 1,
  seed = 1,
  balance = NULL
)

Arguments

frame: Data frame with one row per unit: coordinate columns (lat, lon or x, y, or those named in coords), an optional size column, an optional unit column with names and an optional stratum column.
n: Sample size: a single number (allocated to strata in proportion to the sum of size, or to the number of units when size is NULL), or a vector named by stratum.
size: Column of the size measure for probability-proportional-to-size selection, or NULL for equal probabilities within stratum.
coords: Names of the coordinate columns used for spatial balance (any number of columns for "lpm"; exactly two for "systematic").
strata: Column with the stratum of each unit, or NULL.
method: "lpm", "systematic", "srs" or "cube" (balanced sampling by the cube method of Deville and Tillé 2004, with the fast flight phase and landing by suppression of variables).
replicates: Number of independent interpenetrating replicates for "systematic" (each a systematic sample of about n / replicates units; replicates may share units). Ignored by the other methods.
seed: Seed.
balance: For "cube": names of the columns to balance on (the inclusion probabilities are always included, so the sample size is fixed). The Horvitz-Thompson estimates of these columns match their population totals as closely as the landing allows.

Value

The frame as a tibble with columns pi (inclusion probability in the union of the replicates) and sampled, of class fieldopt_sample, with attributes n, coords, strata, method, seed and, for replicated systematic samples, replicates (a logical matrix, one column per replicate) and pi_replicate (inclusion probability within one replicate).

Details

"lpm": the local pivotal method (Grafström, Lundström and Schelin, 2012), which spreads the sample over the coordinate space so that nearby units are rarely selected together;
"systematic": systematic sampling with probabilities proportional to size along a Hilbert curve through the coordinates (a spatially ordered systematic sample), drawn as replicates independent interpenetrating systematic samples so that a design-based variance can be estimated;
"srs": simple random sampling without replacement.

Spatial balance reduces the variance of totals of spatially structured variables and, at the same time, spreads the field work; the cost model and the routing make that tension explicit.

References

Grafström, A., Lundström, N. L. P. and Schelin, L. (2012). Spatially balanced sampling through the pivotal method. Biometrics, 68(2), 514–520.

Examples

set.seed(1)
cells <- expand.grid(x = 1:20, y = 1:20)
cells$unit <- paste0("c", seq_len(nrow(cells)))
cells$intensity <- cut(
  cells$x + rnorm(400, sd = 3), c(-Inf, 7, 14, Inf),
  c("low", "mid", "high")
)
cells$size <- c(low = 1, mid = 2, high = 4)[cells$intensity]
s <- select_units(cells,
  n = c(low = 10, mid = 15, high = 25), size = "size",
  strata = "intensity"
)
table(s$intensity, s$sampled)
#>       
#>        FALSE TRUE
#>   low    116   10
#>   mid    129   15
#>   high   105   25
r <- select_units(cells, n = 40, method = "systematic", replicates = 4)
dim(attr(r, "replicates"))
#> [1] 400   4